Verified answer

Answer:

Step-by-step explanation:

7^x + 5^y =74 ---- ( 1 )

7^x +1 - 5^y+1 = 218

7^x × 7 - 5^y × 5 = 218 --- ( 2 ) 

let a = 7^x ,

b = 5^y

a + b = 74

a = 74 - b --- ( 3 )

7a - 5b = 218 ---( 4 )

put a value in ( 4 ) ,

7( 74 - b ) - 5b = 218

518 - 7b - 5b = 218

518 - 12b = 218

518 - 218 = 12b

300 = 12b

12b = 300

b = 300 / 12 

b = 25

put b= 25 in equation ( 3 ) ,

a = 74 - 25

a = 49

but 

a  = 49 

7^x = 7²

x = 2 ; 

b = 25 

5^y = 5²

y = 2

∴ x = 2 and y = 2